.TH std::laguerre,std::laguerref,std::laguerrel 3 "2024.06.10" "http://cppreference.com" "C++ Standard Libary"
.SH NAME
std::laguerre,std::laguerref,std::laguerrel \- std::laguerre,std::laguerref,std::laguerrel

.SH Synopsis
   double      laguerre( unsigned int n, double x );

   double      laguerre( unsigned int n, float x );
   double      laguerre( unsigned int n, long double x );  \fB(1)\fP
   float       laguerref( unsigned int n, float x );

   long double laguerrel( unsigned int n, long double x );
   double      laguerre( unsigned int n, IntegralType x ); \fB(2)\fP

   1) Computes the non-associated Laguerre polynomials of the degree n and argument x.
   2) A set of overloads or a function template accepting an argument of any integral
   type. Equivalent to \fB(1)\fP after casting the argument to double.

   As all special functions, laguerre is only guaranteed to be available in <cmath> if
   __STDCPP_MATH_SPEC_FUNCS__ is defined by the implementation to a value at least
   201003L and if the user defines __STDCPP_WANT_MATH_SPEC_FUNCS__ before including any
   standard library headers.

.SH Parameters

   n - the degree of the polynomial, a value of unsigned integer type
   x - the argument, a value of a floating-point or integral type

.SH Return value

   If no errors occur, value of the nonassociated Laguerre polynomial of x, that is

   e^x
   n!

   dn
   dxn

   (xn
   e^-x), is returned.

.SH Error handling

   Errors may be reported as specified in math_errhandling.

     * If the argument is NaN, NaN is returned and domain error is not reported.
     * If x is negative, a domain error may occur.
     * If n is greater or equal than 128, the behavior is implementation-defined.

.SH Notes

   Implementations that do not support TR 29124 but support TR 19768, provide this
   function in the header tr1/cmath and namespace std::tr1.

   An implementation of this function is also available in boost.math.

   The Laguerre polynomials are the polynomial solutions of the equation xy,,
   + (1 - x)y,
   + ny = 0.

   The first few are:

     * laguerre(0, x) = 1.
     * laguerre(1, x) = -x + 1.
     * laguerre(2, x) =

       1
       2

       [x2
       - 4x + 2].
     * laguerre(3, x) =

       1
       6

       [-x3
       - 9x2
       - 18x + 6].

.SH Example

   (works as shown with gcc 6.0)


// Run this code

 #define __STDCPP_WANT_MATH_SPEC_FUNCS__ 1
 #include <cmath>
 #include <iostream>

 double L1(double x)
 {
     return -x + 1;
 }

 double L2(double x)
 {
     return 0.5 * (x * x - 4 * x + 2);
 }

 int main()
 {
     // spot-checks
     std::cout << std::laguerre(1, 0.5) << '=' << L1(0.5) << '\\n'
               << std::laguerre(2, 0.5) << '=' << L2(0.5) << '\\n';
 }

.SH Output:

 0.5=0.5
 0.125=0.125

.SH See also

   assoc_laguerre  associated Laguerre polynomials
   assoc_laguerref \fI(function)\fP
   assoc_laguerrel

.SH External links

   Weisstein, Eric W. "Laguerre Polynomial." From MathWorld--A Wolfram Web Resource.
